The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favour the proposal. Of these, 89 say “Yes.”
(a) Construct and interpret a 99% confidence interval for the proportion of all visitors to Yellowstone who favours the restrictions.
(b) Based on your work in part (a), can the U.S. Forest Service conclude that more than half of visitors to Yellow-stone National Park favour the proposal? Justify your answer.
a. the confidence interval is
Given, the service asks a random sample n =
people who say yes x =
confidence interval for the proportion of all visitors to Yellowstone who favours the restrictions is
From the above part, it is realized that the population extent is somewhere in the range ofand. No, the U.S. Forest Service cant conclude that more than half of visitors to Yellow-stone National Park favour the proposal since the interval has the range . Accordingly, it can't be inferred that the greater part of the guests are supportive of the proposition.
Alcohol abuse has been described by college presidents as the number one problem on campus, and it is an important cause of death in young adults. How common is it? A survey of 10,904 randomly selected U.S. college students collected information on drinking behavior and alcohol-related problems.9 The researchers defined “frequent binge drinking” as having five or more drinks in row three or more times in the past two weeks. According to this definition, 2486 students were classified as frequent binge drinkers.
Interpret the interval in context. Putting It All Together
To assess the accuracy of a laboratory scale, a standard weight known to weigh grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is grams if the scale has no bias). In previous studies, the standard deviation of the scale readings has been about gram. How many measurements must be averaged to get a margin of error of with confidence? Show your work.
64. Vitamin C content Several years ago, the U.S. Agency for International Development provided metric tons of corn-soy blend (CSB) foremergency relief in countries throughout the world. CSB is a highly nutritious, low-cost fortified food. As part of a study to evaluate appropriate vitamin C levels in this food, measurements were taken on samples of CSB produced in a factory. The following data are the amounts of vitamin C,
measured in milligrams per grams (mg/100 g) of blend, for a random sample of size from one production run:Construct and interpret a confidence interval for the mean amount of vitamin C M in the CSB from this production run.
A radio talk show host with a large audience is interested in the proportion of adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the people who phoned in, answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated?
I. The data are a random sample from the population of interest.
II. is so large that both are at least .
III. The population is at least times as large as the sample.
(a) I only
(c) III only
(c) I, II, and III
(b) II only
(d) I and II only
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